tc 146 2 BridgeCrossing(n人过桥问题)
SRM 146 2 1000BridgeCrossing
Problem Statement
A well-known riddle goes like this: Four people are crossing an old bridge. The bridge cannot hold more than two people at once. It is dark, so they can't walk without a flashlight, and they only have one flashlight! Furthermore, the time needed to cross the bridge varies among the people in the group. For instance, let's say that the people take 1, 2, 5 and 10 minutes to cross the bridge. When people walk together, they always walk at the speed of the slowest person. It is impossible to toss the flashlight across the bridge, so one person always has to go back with the flashlight to the others. What is the minimum amount of time needed to get all the people across the bridge?
In this instance, the answer is 17. Person number 1 and 2 cross the bridge together, spending 2 minutes. Then person 1 goes back with the flashlight, spending an additional one minute. Then person 3 and 4 cross the bridge together, spending 10 minutes. Person 2 goes back with the flashlight (2 min), and person 1 and 2 cross the bridge together (2 min). This yields a total of 2+1+10+2+2 = 17 minutes spent.
You want to create a computer program to help you solve new instances of this problem. Given an int[] times, where the elements represent the time each person spends on a crossing, your program should return the minimum possible amount of time spent crossing the bridge.
Definition
- ClassBridgeCrossing
- MethodminTime
- Parametersvector<int>
- Returnsint
- Method signatureint minTime(vector<int> times)
Limits
- Time limit (s)2.000
- Memory limit (MB)64
Notes
- In an optimal solution, exactly two people will be sent across the bridge with the flashlight each time (if possible), and exactly one person will be sent back with the flashlight each time. In other words, in an optimal solution, you will never send more than one person back from the far side at a time, and you will never send less than two people across to the far side each time (when possible).
Constraints
- times will have between 1 and 6 elements, inclusive.
- Each element of times will be between 1 and 100, inclusive.
Test cases
- times{ 1, 2, 5, 10 }
Returns17
The example from the text.- times{ 1, 2, 3, 4, 5 }
Returns16
One solution is: 1 and 2 cross together (2min), 1 goes back (1min), 4 and 5 cross together (5min), 2 goes back (2min), 1 and 3 cross together (3min), 1 goes back (1min), 1 and 2 cross together (2min). This yields a total of 2 + 1 + 5 + 2 + 3 + 1 + 2 = 16 minutes spent.- times{ 100 }
Returns100
Only one person crosses the bridge once.- times{ 1, 2, 3, 50, 99, 100 }
Returns162
#include <cstdio>
#include <cmath>
#include <cstring>
#include <ctime>
#include <iostream>
#include <algorithm>
#include <set>
#include <vector>
#include <sstream>
#include <typeinfo>
#include <fstream> using namespace std;
int ti[] , tot = ;
int a[][] ;
class BridgeCrossing {
public:
int minTime(vector<int> tim) {
tot = ;
for (int i : tim) ti[tot ++] = i ; tot -- ;
sort (ti + , ti + tot + ) ;
// printf ("tot = %d\n" , tot ) ;
// for (int i = 1 ; i <= tot ; i ++) printf ("%d " , ti[i]) ; puts ("") ;
if (tot == ) return ti[] ;
if (tot == ) return ti[] ;
int sum = ti[] ;
for (int i = tot ; i >= ; i -= ) {
if (i == ) {
sum += ti[] + ti[] ;
}
else {
if (ti[] + ti[i - ] < * ti[]) sum += ti[] + ti[i] + ti[] + ti[i - ] ;
else sum += ti[] + ti[i] + ti[] + ti[] ;
}
}
return sum ;
}
}; // CUT begin
ifstream data("BridgeCrossing.sample"); string next_line() {
string s;
getline(data, s);
return s;
} template <typename T> void from_stream(T &t) {
stringstream ss(next_line());
ss >> t;
} void from_stream(string &s) {
s = next_line();
} template <typename T> void from_stream(vector<T> &ts) {
int len;
from_stream(len);
ts.clear();
for (int i = ; i < len; ++i) {
T t;
from_stream(t);
ts.push_back(t);
}
} template <typename T>
string to_string(T t) {
stringstream s;
s << t;
return s.str();
} string to_string(string t) {
return "\"" + t + "\"";
} bool do_test(vector<int> times, int __expected) {
time_t startClock = clock();
BridgeCrossing *instance = new BridgeCrossing();
int __result = instance->minTime(times);
double elapsed = (double)(clock() - startClock) / CLOCKS_PER_SEC;
delete instance; if (__result == __expected) {
cout << "PASSED!" << " (" << elapsed << " seconds)" << endl;
return true;
}
else {
cout << "FAILED!" << " (" << elapsed << " seconds)" << endl;
cout << " Expected: " << to_string(__expected) << endl;
cout << " Received: " << to_string(__result) << endl;
return false;
}
} int run_test(bool mainProcess, const set<int> &case_set, const string command) {
int cases = , passed = ;
while (true) {
if (next_line().find("--") != )
break;
vector<int> times;
from_stream(times);
next_line();
int __answer;
from_stream(__answer); cases++;
if (case_set.size() > && case_set.find(cases - ) == case_set.end())
continue; cout << " Testcase #" << cases - << " ... ";
if ( do_test(times, __answer)) {
passed++;
}
}
if (mainProcess) {
cout << endl << "Passed : " << passed << "/" << cases << " cases" << endl;
int T = time(NULL) - ;
double PT = T / 60.0, TT = 75.0;
cout << "Time : " << T / << " minutes " << T % << " secs" << endl;
cout << "Score : " << * (0.3 + (0.7 * TT * TT) / (10.0 * PT * PT + TT * TT)) << " points" << endl;
}
return ;
} int main(int argc, char *argv[]) {
cout.setf(ios::fixed, ios::floatfield);
cout.precision();
set<int> cases;
bool mainProcess = true;
for (int i = ; i < argc; ++i) {
if ( string(argv[i]) == "-") {
mainProcess = false;
} else {
cases.insert(atoi(argv[i]));
}
}
if (mainProcess) {
cout << "BridgeCrossing (1000 Points)" << endl << endl;
}
return run_test(mainProcess, cases, argv[]);
}
// CUT end这个问题大家都很熟悉吧,晚上有5个人过河,只有一盏灯,,他们每个人的过河时间为1,2,3,6,18(另一组人1,10,10,10,10)。每次最多两个人过河(过河必须有一个人带着灯),且过河的时间按走得慢的那个人算,求5个人过河所需的最少时间?
当然这个问题转到程序里自然是变成了n个人过河喽。
如果你把上面得数据跑了一遍的话,得到29(另一组43)的话。那么心里大概就有最佳方案的笼统概念了:
现在令n个人走过的时间分别为a1,a2,a3,a4,a5,……an;(从小到大)
那么一开始肯定先是1,2过河。
接着考虑花时间最多的那两个人(必须考虑他们,这点很重要),我们怎么送他们呢?
第一种方案:
1回来了,让1把n送过去,然后1回来,再让1把n-1送过去:a1 + an + a1 + a(n-1) ;
第二种方案:
1回来了,让n,n-1过河,然后2回来,再1,2过河: a1 + an + a2 + a2 ;
(如果觉得叙述方案时有奇怪的地方,请见怪不怪,总之是为了让每轮送两人,并且每轮结束时保证1,2都在对岸)
所以这两种方案进行选择时,只要比较:a1 + a(n-1) 和 2× a2 中较小的即可。
。。。大概就是这样,因为每次送两人,所以总人数为奇数时,还有点细节要考虑。
tc 146 2 BridgeCrossing(n人过桥问题)的更多相关文章
- tc 146 2 RectangularGrid(数学推导)
SRM 146 2 500RectangularGrid Problem Statement Given the width and height of a rectangular grid, ret ...
- 蒟蒻修养之tc蓝名计划
开一个新坑......(听说tc是智商高的人才能玩的QAQ显然我是被屠的... 1 [645DIV2]这个能说是裸模拟吗... 弃坑= =做了一些题感觉没必要放上来了= =等div1先吧....... ...
- [转帖][超级少儿不宜]一氧化氮(NO),为什么亚洲人是最硬
阴茎科学:一氧化氮(NO),为什么亚洲人是最硬 尼堪巴图鲁 关注他 2,911 人赞同了该文章 https://zhuanlan.zhihu.com/p/55941740 超级少儿不宜.. ...
- Hznu_oj 2340 你敢一个人过桥吗?
Description 在漆黑的夜里,N位旅行者来到了一座狭窄而且没有护栏的桥边.如果不借助手电筒的话,大家是无论如何也不敢过桥去的.不幸的是,N个人一共只带了一只手电筒,而桥窄得只够让两个人同时过. ...
- 【bzoj2073】[POI2004]PRZ
题目描述 一只队伍在爬山时碰到了雪崩,他们在逃跑时遇到了一座桥,他们要尽快的过桥. 桥已经很旧了, 所以它不能承受太重的东西. 任何时候队伍在桥上的人都不能超过一定的限制. 所以这只队伍过桥时只能分批 ...
- 【BZOJ2073】[POI2004]PRZ 状压DP
[BZOJ2073][POI2004]PRZ Description 一只队伍在爬山时碰到了雪崩,他们在逃跑时遇到了一座桥,他们要尽快的过桥. 桥已经很旧了, 所以它不能承受太重的东西. 任何时候队伍 ...
- 大叔也说并行和串行`性能提升N倍(N由操作系统位数和cpu核数决定)
返回目录 并行是.net4.5主打的技术,同时被封装到了System.Threading.Tasks命名空间下,对外提供了静态类Parallel,我们可以直接使用它的静态方法,它可以并行一个委托数组, ...
- Summarize Series For Burying My College
Summarize Series For Burying My College For Grade ...
- POJ 1700 Crossing River (贪心)
Crossing River Time Limit: 1000MS Memory Limit: 10000K Total Submissions: 9585 Accepted: 3622 Descri ...
随机推荐
- hdu 2010 - 水仙花数
题意: 数学上有个水仙花数,他是这样定义的:"水仙花数"是指一个三位数,它的各位数字的立方和等于其本身,比如:153=1^3+5^3+3^3.现在要求输出所有在m和n范围内的水仙花 ...
- Emmet (Zen Coding) 官方文档中HTML语法的总结
1. 嵌套操作---------- 子操作: > div>ul>li <div> <ul> <li></li> </ul> ...
- Swift开发之 (01) 语法
一 Swift Swift,苹果于2014年WWDC(苹果开发者大会)发布的新开发语言,可与Objective-C*共同运行于Mac OS和iOS平台,用于搭建基于苹果平台的应用程序. Swift是一 ...
- ObjectInputStream类和ObjectInputStream类的使用
版权声明:本文为博主原创文章,未经博主允许不得转载. ObjectInputStream和ObjectInputStream类创建的对象被称为对象输入流和对象输出流. 创建文件输出流代码: FileO ...
- tomcat7.0配置CORS(跨域资源共享)
平时我们做前台页面时可能会遇到浏览器以下提示(浏览器控制台): 已阻止跨源请求:同源策略禁止读取位于 http://xxx.xxx.com 的远程资源.(原因:CORS 头缺少 'Access-Con ...
- Java——表格
import java.awt.event.WindowAdapter; import java.awt.event.WindowEvent; import javax.swing.JFrame; i ...
- Java——文本组件:JTextComponent
import java.awt.GridLayout; import javax.swing.JFrame; import javax.swing.JLabel; import javax.swing ...
- 浏览器本地存储(browser-storage,HTML5-localStorage > IE-UserData > Cookie)
https://www.baidufe.com/component/browser-storage/index.html BrowserStorage是浏览器本地存储的一个解决方案,存储优先级依次为: ...
- Ctrl+Scroll改变所有Editor的缩放比例 (Code::Blocks)
Settings > Editor > Zooming resizes all editors
- 3D Math Library的姿势
http://www.opentk.com/doc/math http://www.gamedev.net/topic/484756-fast-vector-math-library-for-net/ ...